Environmental Engineering Reference
In-Depth Information
(Wexler
1992
). In MATLAB
the formula is computed in an m-file
'analtrans.m'
,
which is described in the following. First input data are specified:
®
Before the formula is implemented, some auxiliary variables are introduced:
e
is a row vector of length
N
. In another row vector
t
the time instants are
gathered, for which the formula is to be evaluated. There are
M
time instants, where
the initial time
t ¼
0 is not counted. In the row vector
x
there are the positions, at
which the formula is evaluated. There are
N
locations, without start- and end-
position. In the row vector
c
the initial condition at
t ¼
0 of the concentration at
the positions
x
is given.
During the execution run of the program the vector
c
becomes a matrix, for
which a new line is created for each of the time-instants given by vector
t
.This
happens in the following loop, in which the formula is implemented:
Theloop-indexis
i
, the current time within the loop is
t(i)
.The
length
function
determines the number of elements in a vector
1
.The
h
is the coefficient 1
D
p
2
,
which appears in the brackets. The lengthy expression in the third and forth line
correspond with the formula of Ogata-Banks. Note that
x
is a vector. In order to add or
subtract the term
vt
(see (
4.4
)) it has to be ensured that the term is also a vector: this is
done by multiplication with the ones-vector
e
. Also note that the multiplication of the
'exp'-factor and the 'erfc'-factor in the last term of the expression has to be performed
element-wise: for that reason the multiplication-operator
.*
is necessary.
=
2
1
Alternatively one may use the
size
function. Here
size(t,2)
replacing
length(t)
works well
also.
size
has the advantage that it can equally be applied to matrices:
size(A)
delivers the number
of rows and columns of array
A
.
2
sqrt
denotes the square root.
